Neutral beam microscopy with a reciprocal space approach using magnetic beam spin encoding

The emerging technique of neutral beam microscopy offers a non-perturbative way of imaging surfaces of various materials which cannot be studied using conventional microscopes. Current neutral beam microscopes use either diffractive focusing or pin-hole scanning to achieve spatial resolution, and are characterised by a strong dependence of the imaging time on the required resolution. In this work we introduce an alternative method for achieving spatial resolution with neutral atom beams which is based on manipulating the magnetic moments of the beam particles in a gradient field, and is characterised by a much weaker dependence of the imaging time on the image resolution. The validity of the imaging approach is demonstrated experimentally by reconstructing one dimensional profiles of the beam which are in good agreement with numerical simulation calculations. Numerical simulations are used to demonstrate the dependence of the signal to noise on the scan resolution and the topography of the sample, and assess the broadening effect due to the spread of velocities of the beam particles. The route towards implementing magnetic encoding in high resolution microscopes is discussed.

The gradient field is produced by 12 parallel wires radially distributed around a ceramic tube (the legend shows the arrangement of the wires in terms of magnitudes and current polarities).The additional homogenous field is produced by a combination of two excitation coils, driving a field through a magnetic core and between two pole pieces located above and below the gradient assembly.The Green arrows Illustrate the direction of the flux induced by the excitation coils, generating  2 .Two vector plots are displayed to illustrate the directionality of the fields generated by both; the gradient wires, and the combination of the gradient wires and  2 within the confines of the 1.5 diameter ceramic tube (not to scale).The inner diameter of the ceramic tube (1.5) was chosen to limit the beam passing through the encoding device to a region where the gradient is sufficiently homogeneous.

Figure S1 .
Figure S1.Homogeneity of the gradient within the magnetic encoding device.Contour plot of    (, ) calculated using magnetic field profiles generated through finite-element modelling of the  = 12 gradient field assembly (in ANSYS Maxwell).The black circle illustrates the 1.5 diameter of the central region, corresponding to the dimensions of the ceramic tube (illustrated in figure S4) which effectively confines the maximal position of the beam particles.The flatness of the central region indicates good gradient field homogeneity.

Figure S2 .
Figure S2.Full experimental signals for configuration A. All 4 S(  ) measurements (solid represents the real and dotted the imaginary components of the signal) along with the corresponding spatial profile reconstructions ρ 1D ().Error bars were calculated from the standard deviation of repeat measurements.

Figure S3 .
Figure S3.Full experimental signals for configuration B. All 4 S(  ) measurements (solid represents the real and dotted the imaginary components of the signal) along with the corresponding spatial profile reconstructions ρ 1D ().Error bars were calculated from the standard deviation of repeat measurements.

Figure S4 .
Figure S4.Schematic of magnetic encoding device.The gradient field is produced by 12 parallel wires radially distributed around a ceramic tube (the legend shows the arrangement of the wires in terms of magnitudes and current polarities).The additional homogenous field is produced by a combination of two excitation coils, driving a field through a magnetic core and between two pole pieces located above and below the gradient assembly.The Green arrows Illustrate the direction of the flux induced by the excitation coils, generating  2 .Two vector plots are displayed to illustrate the directionality of the fields generated by both; the gradient wires, and the combination of the gradient wires and  2 within the confines of the 1.5 diameter ceramic tube (not to scale).The inner diameter of the ceramic tube (1.5) was chosen to limit the beam passing through the encoding device to a region where the gradient is sufficiently homogeneous.

Figure S5 .
Figure S5.Simulating the effect of resolution enhancement on the SNR of images reconstructed using magnetic encoding.The top row illustrates the   ,   measurement points required for 5 different resolution enhancement factors (N=1,2,4,6,8) corresponding to meshes with 10x10 (left side) up to 80x80 (right side) elements.The middle and lower rows show reconstructions of (, ) ℎ and (, ) ℎ respectively, for these 5 different resolutions.The difference between the images shown in this figure and those shown in figure6, in the main text, are that the measurement time for an individual   ,   point has been kept fixed, i.e. higher resolutions have been allowed a longer total simulated measurement time.

Figure S6 .
Figure S6.Block diagram for 1d and 2d image generation.Experimental protocols for magnetic encoded imaging performed in 1dimension and 2-dimension respectively (from top to bottom).